Universality and herd immunity threshold: Revisiting the SIR model for COVID-19

Sourav Chowdhury (), Suparna Roychowdhury and Indranath Chaudhuri ()
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Sourav Chowdhury: Department of Physics, St. Xavier’s College (Autonomous), 30 Mother Teresa Sarani, Kolkata 700016, West Bengal, India
Suparna Roychowdhury: Department of Physics, St. Xavier’s College (Autonomous), 30 Mother Teresa Sarani, Kolkata 700016, West Bengal, India
Indranath Chaudhuri: Department of Physics, St. Xavier’s College (Autonomous), 30 Mother Teresa Sarani, Kolkata 700016, West Bengal, India

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 10, 1-33

Abstract: COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-mentioned quantities to find the reasons behind the re-outbreak of this disease. Also, the effectiveness of herd immunity to prevent an epidemic has been analyzed with respect to this model. We have also tried to show that there are certain universal aspects in the spread and containment of the disease in various countries for a short period of time. Finally, we have also analyzed the current pandemic situation in India and have attempted to discuss the possibilities in order to predict its future behavior using our model.

Keywords: SIR model; reproduction number; herd immunity; herd immunity threshold; universality; re-infection; intervention (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S012918312150128X

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